See this earlier answer for examples of how to access the underlying raw response types.
Also the C# ServiceClient wiki is the authoritative documentation on ServiceStack's built in C#/.NET service clients. It includes a section on different ways of accessing the underlying raw response, including via the Response stream:
using (Stream responseStream = client.Get<Stream>("/poco/World")) {
var dto = responseStream.ReadFully().FromUtf8Bytes().FromJson<PocoResponse>();
dto.Result //Hello, World
}